Thursday, July 26, 2007

theorems (parallelpgram)

Quadrilateral
----Let A,B,C and D be four points on the same plane, if no three of these points are collinear and the segments line segment AB, BC, CD and AD intersect only at their endpoints, then the union of these four segmenst is called a quadrilateral.

Theorem 6-14 PDCT
--> Each diagonal seperates a parallelogram into 2 congruent triangles.

Theorem 6-15 POSC
--> In a parallel, any 2 opposite sides are congruent.

Theorem 6-16 POAC
--> In a parellelogram, any 2 opposite angles are congruent.

Theorem 6-17 PCAS
--> In a parallelogram, any 2 consecutive angles are supplementary.

Theorem 6-18 PDB
--> The diagonals of a parallelogram bisect each other.

Theorem 6-19 DSCP
--> Given a quadrilateral in which both pairs of opposite sides are congruent, then the quadrilateral is a parallelorgram.

Theorem 6-20 SPDC
--> If 2 sides of a quadrilateral are parallel and congruent then the quadrilateral is a parallelogram

Theorem 6-21 DBP
--> If the diagonals of a quadrilateral bisect each other, then a quadrilateral is a parallelogram.

Theorem 6-22 The Middline Theorem
--> The segment between the midpoints of two sides of a triangle is parallel to the 3rd side and is half as long.

theorem (triangles ang transversal)

Theorem 6-5 AIP (Alternate Interior Parallel)
--> Given 2 lines cut by a transversal. If a pair of alternate interior angles are congruent, then the lines are parallel.

Theorem 6-6
--> Given 2 lines cut by a transversal. If a pair of coresponding angles are congruent then a pair of corresponding angles are congruent, then a pair of alternate interior angles are congruent.

Theorem 6-7
--> Given 2 lines cut by a transversal. If a pair of corresponding angles are congruent then the lines are parallel.

Theorem 6-8
--> Given 2 lines cut by a transversal. Of a pair pf interior angles on the same side of the transversal are suplementary, the lines are parallel.

Theorem 6-9 The PAI Theorem
--> If 2 parallel lines are cut by a transversal, then the alternate interior angles are congruent.

Corollary 6-9.1 The PCA Corollary
--> If 2 parallel lines are cut by a transversal, then each pair of corresponding angles are congruent.

Corollary 6-9.2
--> If 2 parallel lines are cut by a transversal, the interior angles on the same side of the transversal are suplementary.

6-8 IASP / Consecutive Interior Angles suplementary
6-8.1 CESP/ COnsecutive Exterior Angles Suplementary
AEP/ Alternate Exterior Angles Parallel

Theorem 6-10
--> In a plane, if a line intersects one of two parallel lines in only one point, then it intersects the other.

Theorem 6-11
--> In a plane, if two lines are each parallel to a third line then they are parallel to each other.

Theorem 6-12
--> In a plane, if a line is perpendicular to one of two parallel lines it is perpendicular to one of two parallel lines it is perpendicular to the other.

Theorem 6-13
--> For every triangle, the sum of the measures of the interior angles is 180

6-13.1
--> Given a correspondence between two triangles if two pairs of corresponding angles are congruent, then the 3rd pair of corresponding angles are also congruent.

6-13.2
--> The acute angles of a right triangle are coplementary.

6-13.3
--> For any triangles, the measure of any exterior angles the sum of the two remote interior angles.

theorems (lines and planes)

Theorem 6-1
--> Two parallel lines lie in exactly one plane

Theorem 6-2
--> In a plane, two lines are parallel if they are both perpendicular at the same line.

Theorem 6-3
--> Let L be a line and let P be a point NOT on L. There is at least one line through P parallel to L.

Theorem 6-4
--> If 2 lines are cut by a transversal and one pair of alternate interior angles are congruent, then the other pair of alternate angles are also congruent.